Problem: Solve for $x$ and $y$ using elimination. ${-x-4y = -35}$ ${-x-5y = -43}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${x+4y = 35}$ $-x-5y = -43$ Add the top and bottom equations together. $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-x-4y = -35}\thinspace$ to find $x$ ${-x - 4}{(8)}{= -35}$ $-x-32 = -35$ $-x-32{+32} = -35{+32}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 8}$ into $\thinspace {-x-5y = -43}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(8)}{= -43}$ ${x = 3}$